Japanese Patent Publication No. 2006-343983 discloses a fire alarm system composed of a master station and a plurality of battery-powered fire detecting terminals each equipped with a fire sensor. The fire detecting terminals are linked to the master station for wireless communication with each other for transmitting a fire occurrence data. In order to achieve a reliable and sophisticated information exchange without causing an interference between the fire detecting terminals, a TDMA (time division multiple access) scheme is utilized for synchronous radio communication among the fire detecting terminals and the master station. While the system is required to keep operating over an extended period of time, such TDMA scheme is rather power-consuming to shorten a battery-life and therefore necessitates frequent replacement of the battery, which is inconvenient for system which is expected to see only a very few chance of fire occurrence during its life time.